Currently, in the semiconductor industry there is a great interest in the characterization of thin films. Integrated circuits are made up a large number of thin films deposited onto a semiconductor substrate, such as silicon. The thin films include metals to make connections between the transistors making up the chip, and insulating films to provide insulation between the metal layers (see: S. A. Campbell, The Science and Engineering of Microelectronic Fabrication, Oxford University Press, (1996)). The metal films (interconnects) are typically arranged as a series of patterned layers. At the present time there may be 4 or 5 layers of interconnects. It is likely that as more complex integrated circuits are developed which will require a greater number of interconnections the number of layers will increase. Metals of current interest include, for example, aluminum, copper, titanium and silicides. Insulating films include, for example, oxide glasses of various compositions and polymers.
When a stress is applied to a material there is a change in shape of the material which can be described by means of the strain tensor. Different materials, and even the same material at different temperatures, or prepared by a different method, exhibit a different response to an applied stress (see: F. A. McClintock and A. Argon, Mechanical Behavior of Materials, Addison-Wesley, (1965)).
For an elastic material when the stress is removed the material returns to its original size and shape. For such materials there is a range of stress over which the strain is, to a good approximation, linearly proportional to the applied stress. Within this range of stress such materials are said to be linearly elastic. In the regime of linear elasticity the material is characterized by a number of parameters called elastic constants. These parameters are coefficients which relate the elements of the stress tensor to elements of the strain tensor. The elastic constants are dependent on the composition of the material. They may also be affected to some extent by the microstructure of the material. This microstructure, in turn, is influenced by the manner in which the material is prepared. The microstructure includes the crystalline phase, the size and orientation of crystalline grains, the presence and arrangement of dislocations and point defects within the material.
All materials show substantial deviations from elastic behavior when the stress exceeds some value. Such materials are referred to as anelastic. For these materials, the material does not return to its original size or shape after application of a stress. The strain that results from the application for a period of time .tau..sub.stress of a stress of a given magnitude .sigma. depends in a complicated way on the value of .tau..sub.stress and .sigma.. For some materials there is no permanent change in shape or size unless a exceeds a critical value .sigma..sub.yield ; this stress is referred to as the yield stress for the onset of plastic flow. For other materials the application of even a small stress results in a small strain which increases steadily with the time .tau..sub.stress. For anelastic materials the response of the material to an applied stress will, in general, be substantially affected by the history of the sample. For example, a sample may show a different response to an applied stress of given magnitude according to the number of times that the stress has been applied. For an anelastic material the complete characterization of the mechanical properties is much more complicated than for an elastic material. The anelastic properties are affected considerably by the microstructure of the material. The anelastic behavior of a film may also be significantly influenced by the thickness and other dimensions of the film and possibly also by the properties of the films adjacent to it, or by the substrate if the film is directly deposited onto the substrate. Generally, it is more likely that anelasticity will be important the higher the temperature of the sample.
Stress in thin films making up an integrated circuit can arise from a number of mechanisms. These include the following.
(A) The film may be deposited at an elevated temperature onto the substrate, or on top of another film deposited previously. When the resulting structure is cooled the difference between the thermal expansion coefficient of the substrate and the deposited film will result in the film being under stress.
(B) The film may be deposited by a process that results in a built-in stress, even if the film is grown at ambient temperature. For example, if a crystalline film is grown epitaxially on a substrate there will generally be a stress that arises from the difference in the unstrained lattice parameters of the two materials.
(C) After a film is grown it may be subject to further processing which changes the stress in the film. For example, ion irradiation or plasma bombardment can cause the stress in a film to be modified.
(D) When an electrical current flows through a metal film a different type of stress can result (see: C. Bosvieux and J. Friedel, Journal of Physics and Chemistry of Solids, Volume 23,123,(1962); see also: H. B. Huntington and A. R. Grone, Journal of Physics and Chemistry of Solids, Volume 20,76,(1961)) The interaction between the current and the atoms in the film can result in a force on the atoms. This force can be considered to be a form of stress at the microscopic level. This stress can result in a permanent displacement of the atoms from their original positions referred to as electromigration. This displacement of the atoms can result in a change in the external shape and dimensions of the film. This change in shape and dimensions can be considered to amount to a special type of plastic strain.
It is desirable to have available a method to characterize the mechanical properties of thin films.
This invention is concerned with the response of thin films to an applied stress, including stresses that result in plastic flow of the film. Previously, the following methods have been used for characterization of the mechanical properties of thin films. In a first method, the film may be deposited onto a substrate having a thermal expansion coefficient different than the thermal expansion coefficient of the thin film. The temperature of the substrate is then raised. Because of the difference between the thermal expansion coefficient of the film and the expansion coefficient of the substrate, the film is strained with respect to its stress-free state at the same temperature. The stress in the film can be determined by measuring the curvature that is induced in the wafer. (See: M. F. Doerner, D. S. Gardner and W. D. Nix, Journal of Materials Research, Volume 1, 845-851, (1986), (hereafter Doerner et al.) and C. A. Volkert, C. F. Alofs and J. R. Liefting, Journal of Material Research, Volume 9, 1147-1155 (1994)). The curvature is commonly measured either via a differential capacitance technique or by laser deflection. Consider a film which lies in the xy-plane and whose surface is normal to the z-direction. The radius of curvature R of the wafer is measured together with the thickness d of the film and the thickness d.sub.s of the substrate. The non-zero components of the stress tensor of the film are then .sigma..sub.zz =0, .sigma..sub.xx =.sigma..sub.yy =-P, where P is found from the relation EQU P=(Y.sub.s d.sub.s.sup.2)/[6R(1-.nu..sub.s)d] (1)
where Y.sub.s is Young's modulus for the substrate and .nu..sub.s is Poisson's ratio for the substrate. If the substrate takes on a shape which is convex on the side where the film is deposited this indicates that the stress is compressive, (i.e. P is positive and the stress is negative).
In this measurement the temperature can be changed continuously, or in discrete steps, so as to change the strain. The radius of curvature R is measured continuously and the stress calculated. Thus the stress-strain relation can be determined. This method has two disadvantages: (i) the relationship between stress and strain at a fixed definite temperature cannot be determined because in order to produce the strain it is necessary to vary the temperature; (ii) the measurement of wafer curvature can only be used to give the average stress over a large area of the film. It cannot be used to measure stress within a small region of a film, or to find the stress in a film deposited onto a small area of the substrate.
A second method of the prior art, uses a nanoindenter to perform hardness measurements. A very small indenter tip is pressed into the film. (See: Doerner et al.) The force applied to the tip and the tip displacement are measured. This method has the disadvantage that the stress and the strain have a complicated spatial variation in the vicinity of the tip, i.e. they are not uniform throughout the film. This complicates the analysis and interpretation of the measurements.
A third method of the prior art, uses electron microscopy to measure the changes in the film geometry that result from applied stress. When the stress applied to a film exceeds the yield stress and plastic flow occurs, the surface of a film often becomes uneven and this can be detected by electron microscope observations. Similarly, electromigration often results in the appearance of characteristic features, such as hillocks, on the surface of films. (See: I. A. Blech and E. S. Meieran, Journal of Applied Physics, Volume 40, 485-491 (1969)). Scanning electron microscopy has the disadvantage that significant time is required to make a measurement. A second difficulty is that conventional scanning electron microscopes often cannot accommodate the large diameter wafers (200 or 300 mm) that are involved in modern chip fabrication. It is also possible to use transmission electron microscopy to measure changes in microstructure that result from plastic deformation and electromigration. However, this measurement requires either that the film be removed from the substrate or that special samples be prepared in which the substrate underneath some part of the length of a metal film is etched away.
In a fourth method of the prior art, the film or films of interest are completely or partially removed from the substrate. Mechanical contact is made to the film in some way and stress is then directly applied. The resulting strain is then measured. This method has the disadvantage that since the film is removed from the substrate the sample is destroyed.